Average Error: 0.3 → 0.3
Time: 9.0s
Precision: 64
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]
double f(double x_re, double x_im, double y_re, double y_im) {
        double r393088 = x_re;
        double r393089 = y_re;
        double r393090 = r393088 * r393089;
        double r393091 = x_im;
        double r393092 = y_im;
        double r393093 = r393091 * r393092;
        double r393094 = r393090 - r393093;
        return r393094;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r393095 = x_re;
        double r393096 = y_re;
        double r393097 = r393095 * r393096;
        double r393098 = x_im;
        double r393099 = y_im;
        double r393100 = r393098 * r393099;
        double r393101 = r393097 - r393100;
        return r393101;
}


x.re \cdot y.re - x.im \cdot y.im
↓
x.re \cdot y.re - x.im \cdot y.im

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

  1. Initial program 0.3

    \[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]

  2. Final simplification0.3

    \[\leadsto x.re \cdot y.re - x.im \cdot y.im\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))